#### Q09 Part V: Linear Regression • Name:

Lane lengths
Lane Length/m
1421
2426
3431
4434
5444
6460
7458
6452
5447
4436
3428
2423
1410

Using a Global Positioning Satellite unit I ran laps at the Pohnpei state track up at PICS starting in lane one and moving out by one lane per lap until the seventh lane and then I moved in by one lane per lap. The data is given in the table. The first column is the lane number, the second column is the length of that lane.

1. _________ Determine the sample size of the lane length in meters.
2. _________ Determine the minimum lane length in meters.
3. _________ Determine the maximum lane length in meters.
4. _________ Determine the range of the lane length in meters.
5. _________ Determine the mode of the lane lengths in meters.
6. _________ Determine the median of the lane lengths in meters.
7. _________ Determine the mean of the lane lengths in meters.
8. _________ Determine the standard deviation of the lane lengths in meters.
9. _________ Determine the coefficient of variation of the lane lengths in meters.
10. _________ Calculate the slope of the best fit (least squares) line.
11. _________ Calculate the y-intercept of the best fit (least squares) line.
12. _________ Is the correlation positive, negative, or neutral?
13. _________ Use the equation of the best fit line to calculate the predicted lane length for lane eight.
14. _________ If there was a lane "zero", how long would lane zero be predicted to be?
15. _________ Use the inverse of the best fit line to calculate the lane number which is 500 meters long (a half a kilometer).
16. _________ Calculate the linear correlation coefficient r for the data.
17. _________ Is the correlation none, low, moderate, high, or perfect?
18. _________ Calculate the coefficient of determination.
19. _________ What percent of the variation in the lane number explains the variation in the lane length?
Linear Regression Statistics
Statistic or ParameterSymbolEquationsOpenOffice
Slopeb=SLOPE(y data; x data)
Intercepta=INTERCEPT(y data; x data)
Correlationr=CORREL(y data; x data)
Coefficient of Determinationr2  =(CORREL(y data; x data))^2